As further generalizations of Uq(sl2), an interesting class of algebras Uq(f(K,H)) was introduced and studied in [10]. In this paper, we further study these algebras by realizing them as Hyperbolic algebras. Such a realization yields a natural construction of interesting families of irreducible representations of Uq(f(K,H)) by using methods in non-commutative algebraic geometry([16]). We also i...

Covariant tensor representations of glm|n occur as irreducible components of tensor powers of the natural (m + n)-dimensional representation. We construct a basis of each covariant representation and give explicit formulas for the action of the generators of glm|n in this basis. The basis has the property that the natural Lie subalgebras glm and gln act by the classical Gelfand–Tsetlin formulas...

We prove a nonsymmetric analogue of a formula of Kato and Lusztig which describes the coefficients of the expansion of irreducible Weyl characters in terms of (degenerate) symmetric Macdonald polynomials as certain Kazhdan–Lusztig polynomials. We also establish precise polynomiality results for coefficients of symmetric and nonsymmetric Macdonald polynomials and a version of Demazure’s characte...

A conjugacy class C of a finite group G is a sign conjugacy class if every irreducible character of G takes value 0, 1 or −1 on C. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.

Let H denote a semisimple Hopf algebra over an algebraically closed field k of characteristic 0. We show that the degree of any irreducible representation of H whose character belongs to the center of H∗ must be a divisor of dimk H .

It is shown that there are infinitely many formulas to calculate multiplicities of weights participating in irreducible representations of AN Lie algebras. On contrary to the recursive character of Kostant and Freudenthal multiplicity formulas, they provide us systems of linear algebraic equations with N-dependent polinomial coefficients. These polinomial coefficients are in fact related with p...

We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In particular, these points are non-integral and detect a Seifert surface.

Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of Hansen-Mullen.

A level-one representation of the quantum affine superalgebra U q (sl(M + 1|N + 1)) and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of level-one irreducible highest weight modules of U q (sl(2|1)) are conjectured.

Fermionic-type character formulae are presented for charged irreducible modules of the graded parafermionic conformal field theory associated to the coset ôsp(1, 2)k/û(1). This is obtained by counting the weakly ordered ‘partitions’ subject to the graded Z̃k exclusion principle. The bosonic form of the characters is also presented.